3. A company needs to ship its product from three plants to four warehouses and wants to minimize the total transportation costs. The transportation costs are provided in the following table. Further requirements are: Plant 1 has a capacity limit of 10,000 items Plant 2 has a capacity limit of 12,000 items Plant 3 has a capacity limit of 15,000 items Warehouse A wants at least 7,000 items Warehouse B wants at least 15,000 items Warehouse C wants at least 10,000 items Warehouse D wants at least 5,000 items.

a) Define the decision variables.

b) Write the objective function.

c) Write the constraints in standard form.